Electrons and some nuclei possess a quantized unit of angular momentum called xe2x80x9cspinxe2x80x9d. This invention concerns electron devices for single electron and nuclear spin measurement.
The |↑↓ greater than  notation is used here to represent the electron spin state, and the |01  greater than  notation the nuclear state. For simplicity, normalization constants are omitted.
In two electron systems, the electron spins may be aligned (total spin angular momentum =1) in triplet states (|↓↓ greater than , |↑↑ greater than , and |↑↓+↓↑ greater than ) or opposed (total spin angular momentum=0 ) in a singlet state (|↑↓xe2x88x92↓↑ greater than ). Similarly the nuclear spins may be aligned or opposed. In the |↓↓11 greater than  state, all spins point in the same direction.
In the laboratory, large numbers (xe2x89xa71023) of electron and nuclear spins are regularly probed using traditional magnetic resonance techniques.
There are important applications for devices and techniques that can measure a single electron or nuclear spin. For example, magnetic resonance experiments could be performed on a single atom or molecule and the local environment (electric and magnetic fields) could be measured with great precision. Alternatively, single electron or nuclear spins could be used as qubits in a quantum computer. Single spin measuring devices would be required in the computer to initialize and to measure the single-spin qubits.
A first aspect of the invention is an electron device for single spin measurement, comprising:
A semiconductor substrate into which at least one donor atom is introduced to produce a donor nuclear spin electron system having large electron wave functions at the nucleus of the donor atom.
An insulating layer above the substrate.
A first conducting gate on the insulating layer above the donor atom to control the energy of the bound electron state at the donor.
A second conducting gate on the insulating layer adjacent the first gate to generate at least one electron in the substrate.
In use, a single electron is bound to the donor, and the donor atom is weakly coupled to the at least one electron in the substrate. The gates are biased so that the at least one electron in the substrate will move to the donor, but only if the spins of the at least one electron and the donor are in a relationship which permits the movement.
The arrangement is such that detection of current flow, or even movement of a single electron, in the device constitutes a measurement of a single spin.
The motion of a single electron may be detected by probing the system capacitively, for instance by using single electron capacitance probes, and any metallic lead can couple to the system, with no special requirement for spin-polarized electrons. Alternatively, the charge motion may be detected by single electron tunnelling transistor capacitance electrometry.
A first example of the invention is an electron device for single electron spin measurement, comprising:
A semiconductor substrate into which at least one donor atom is introduced to produce a donor nuclear spin electron system having large electron wave functions at the nucleus of the donor atom.
An insulating layer above the substrate.
A conducting A-gate on the insulating layer above the donor atom to control the energy of the bound electron state at the donor.
A conducting E-gate on the insulating layer on either side of the A-gate to generate a reservoir of spin polarised electrons at the interface between the substrate and the insulating layer.
In use the donor atom is weakly coupled to the two reservoirs of spin-polarized electrons, both reservoirs have the same polarisation, and a single electron, whose spin is to be determined, is bound to the donor. The E-gates are biased so that current will flow between them, but only if the spin on the donor is opposite to the spin polarization in the reservoirs. In this case one electron at a time from one of the reservoirs may join the same quantum state (with opposite spin) as the bound electron, and then depart the donor to the other reservoir. But when the electrons are all polarized in the same direction no current can flow since the electrons from the reservoir cannot enter the same quantum state as the bound electron.
In another example, there are two donors with xe2x80x98A-gatesxe2x80x99 located above each of them, and an xe2x80x98E-gatexe2x80x99 located between them. Electrons are bound to the two, positively charged, donors, and the donors are spaced sufficiently close to each other so that electron transfer, or exchange coupling, between them is possible.
In use, an increasing potential difference is applied to the two A-gates and at some point it will become energetically favorable for both electrons to become bound to the same donor, but only if the electrons are in a mutual singlet state. The signature of the singlet state, charge motion between donors as a differential bias is applied to the A-gates, can be detected externally.
Another example of the invention is an electron device for single nuclear spin measurement, comprising:
A semiconductor substrate into which at least one donor atom is introduced to produce a donor nuclear spin electron system having large electron wave functions at the nucleus of the donor atom.
An insulating layer above the substrate.
A conducting A-gate on the insulating layer above the donor atom to control the energy of the bound electron state at the donor.
A conducting E-gate on the insulating layer on either side of the A-gate to generate a reservoir of electrons at the interface between the substrate and the insulating layer.
Where all the electron spins are polarized in the same direction, and the donor is a nucleus with spin, coupled to the electrons by the hyperfine interaction. The E-gates are biased so that current will flow between them, but only if the the nuclear spin is initially opposed to the electron spins. The process involves the electron coming from the reservoir and exchanging its spin with the spin of the nucleus so that its spin is then opposed to the donor electron and can form a singlet with it. The arrangement is such that detection of movement of a single electron in the device constitutes a measurement of the nuclear spin on the donor.
Alternatively, since the transport of an electron onto the donor and off again involves two spin flips, a current flow across the donor preserves nuclear spin polarisation, and current flow is turned on or off depending on the orientation of the nuclear spin on the donor.
The electrons may, for example, be polarised by being at low temperature in a large magnetic field.
The conducting E-gate on the insulating layer on either side of the A-gate may generate a 2-Dimensional electron gas at the interface between the substrate and the insulating layer.
In use, the E-gates may be biased so that only |↓ greater than  electrons are present on both sides of the donor atom. And the A-gate may be biased so that EF lies at the energy of the two electron bound state at the donor (the Dxe2x88x92 state).
The host may contain only nuclei with spin I=0, such as Group IV semiconductors composed primarily of I=0 isotopes and purified to contain only I=0 isotopes. Si is an attractive choice for the semiconductor host. The donor can be 31P.
The gates may be formed from metallic strips patterned on the surface of the insulating layer. A step in the insulating layer over which the gates cross may serve to localise the gates electric fields in the vicinity of the donor atoms.
The state of a given spin system may be inferred from the measurement if the system is prepared by adiabatic changes to the spin state energies before the measurement takes place, to ensure that the measurement outcome is determined by the initial state of a given spin.
Another aspect of the invention is a procedure for the preparation of spin states in a two electron system, which comprises the following steps:
First, manipulate the A-gates so that a first spin has larger energy than a second spin.
Next, apply bias to the intermediary E-gate to turn on the exchange coupling between the two electrons. As the exchange coupling increases, the lower energy state of the two states with a single spin pointing up evolves into the singlet state which at large E will have the lowest energy.
Then bring the A-gates back into balance so that the ground state is an exact singlet.
A measurement will yield the result for a singlet state if and only if the original spin configuration was (↓↑). After the measurement the two spins can be returned to their initial configuration by reversing the sequence of adiabatic manipulations.
If the state of the first spin is unknown, two measurements can be performed in sequence on the spins, with the second beginning with a spin flip of the first spin. The second measurement will produce a singlet result if and only if the initial state, prior to the first measurement, was (↑↑).
Examples of the invention can be incorporated into a quantum computer which has:
A semiconductor substrate into which donor atoms are introduced to produce an array of donor nuclear spin electron systems having large electron wave functions at the nucleus of the donor atoms.
An insulating layer above the substrate.
Conducting A-gates on the insulating layer above respective donor atoms to control the strength of the hyperfine interactions between the donated electrons and the donor atoms"" nuclear spins, and hence the resonance frequency of the nuclear spins of the donor atoms.
Conducting J-gates on the insulating layer between A-gates to turn on and off electron mediated coupling between the nuclear spins of adjacent donor atoms.
Where, the nuclear spins of the donor atoms are the quantum states or xe2x80x9cqubitsxe2x80x9d in which quantum information is stored and manipulated by selective application of voltage to the A-and J-gates and selective application of the alternating magnetic field to the substrate.
A cooling means to maintain the substrate cooled to a temperature sufficiently low. In operation the temperature of the device may be below 100 millikelvin (mk) and will typically be in the region of 50 mK. The device is non-dissipative and can consequently be maintained at low temperatures during computation with comparative ease. Dissipation will arise external to the computer from gate biasing and from eddy currents caused by the alternating magnetic field, and during polarisation and detection of nuclear spins at the beginning and end of the computation. These effects will determine the minimum operable temperature of the computer.
A source of constant magnetic field having sufficient strength to break the two-fold spin degeneracy of the bound state of the electron at the donor. The constant magnetic field may be required to be of the order of 2 Tesla. Such powerful magnetic fields may be generated from superconductors.
The combination of cooling and magnetic field ensures the electrons only occupy the nondegenerate lowest spin energy level.
A source of alternating magnetic field of sufficient force to flip the nuclear spin of donor atoms resonant with the field, and means to selectively apply the alternating magnetic field to the substrate. And means to selectively apply voltage to the A-and J-gates.
The E-gates may be separate from the J-gates, or they may be incorporated in them.
Single electron tunnelling transistors (SETTs) are currently the most sensitive devices developed to measure small charges and small charge motions. SETTs contain a small xe2x80x9cislandxe2x80x9d electrode located between source and drain electrodes. Current flows from source to drain only if there is an energy level in the island equal to the Fermi level in the source and drain. A xe2x80x9cCoulomb blockadexe2x80x9d results when no energy level is available on the island through which the electrons can tunnel. The extreme sensitivity of SETTs will occur when the island is extremely small and when the device is at low temperature.
The metal electrodes may lie on the top of the Si substrate, containing P donors located below the electrodes. Motion of charge between the donors changes the potential of the SETT island, and hence its conductance. The conductance of the SETT, when the gate is biased appropriately, constitutes a measurement from which electron or nuclear spin can be inferred, using arguments presented above.
One of the A-gates may also be the island of a SETT. In the scenario where the devices discussed above are used to measure and initialize spins in a quantum computer, many SETTs would be necessary to measure many spins simultaneously. The capacitive coupling technique for spin measurement is particularly attractive, since a two dimensional array of spins could be measured using electrodes out of the plane of the spins, and every spin in the array could be independently measured by a separate SETT device. Thus, this approach to spin measurement is well suited to future large scale quantum computation.